Discovering efficient periodic behaviors in mechanical systems via neural approximators

Yannik P. Wotte*, Sven Dummer, Nicolò Botteghi, Christoph Brune, Stefano Stramigioli, Federico Califano

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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It is well known that conservative mechanical systems exhibit local oscillatory behaviors due to their elastic and gravitational potentials, which completely characterize these periodic motions together with the inertial properties of the system. The classification of these periodic behaviors and their geometric characterization are in an ongoing secular debate, which recently led to the so-called eigenmanifold theory. The eigenmanifold characterizes nonlinear oscillations as a generalization of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed-loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient-descent methods involving neural networks. Extensive simulations show the validity of the approach.
Original languageEnglish
Pages (from-to)3052-3079
Number of pages28
JournalOptimal Control Applications and Methods
Issue number6
Early online date22 Jun 2023
Publication statusPublished - Nov 2023


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